Similar equations were obtained in [1]} where the investigations were done for general D3 brane solutions in the \(AdS_5 \times S^5\)  spacetime. In [2]} it was shown that the holographic duals of codimension-2 defects in 4d \(\mathcal {N}=4\)  SYM belong to same class of BPS solutions that also admit giant gravitons and the dual-giant gravitons from [1]}. In [4]} general giant M2 brane solutions which have two non-zero spin charges along \(S^4\)  were discussed in \(AdS_7 \times S^4\)  and they were atleast \(\frac{1}{4}\) -BPS. These solutions were obtained when at any given time the spatial part of M2 worldvolume is given by the intersection of a holomorphic curve \(C\)  in \(\mathbb {C}^2\)  space with \(S^4\)  sphere. Where the \(S^4\)  was considered to be embedded in the \(5d\)  flat space \(\mathbb {R}^5 = \mathbb {C}^2 \times \mathbb {R}\) .
